Cos Inverse Calculator
Use this professional cos inverse calculator to find the inverse cosine value of any number between -1 and 1. The tool instantly gives your answer in both degrees and radians, making it useful for trigonometry, geometry, engineering, and math practice.
Calculate cos-1(x)
What Is a Cos Inverse Calculator?
A cos inverse calculator helps you find the angle when the cosine value is already known. In mathematics, cos inverse is also called arccos or inverse cosine. It is written as cos-1(x), where x must be a value between -1 and 1.
For example, if the cosine value is 0.5, the inverse cosine is 60 degrees or approximately 1.0472 radians. This calculator saves time by converting the value accurately without manual trigonometric table lookup.
Cos Inverse Formula
The formula used by this tool is:
Here, x is the cosine value, and θ is the angle returned in degrees and radians.
How It Works
This inverse cosine calculator follows a simple mathematical process to return clean and accurate results.
1. Enter a Value
Type any cosine value from -1 to 1. Values outside this range are not valid for real inverse cosine.
2. Apply arccos
The calculator uses the arccos function to find the angle that matches your entered cosine value.
3. Get Results
Your answer is displayed in degrees and radians so you can use it for different math requirements.
Common Cos Inverse Values
Here are some commonly used inverse cosine values that are helpful in trigonometry problems.
| Cosine Value | cos-1(x) in Degrees | cos-1(x) in Radians |
|---|---|---|
| -1 | 180° | π rad |
| -0.5 | 120° | 2π / 3 rad |
| 0 | 90° | π / 2 rad |
| 0.5 | 60° | π / 3 rad |
| 1 | 0° | 0 rad |
FAQs
Quick answers about using the cos inverse calculator.
What does cos inverse mean?
Cos inverse means finding the angle when the cosine value is known. It is written as cos-1(x) or arccos(x).
What values can I enter in this calculator?
You can enter any number from -1 to 1. In real-number trigonometry, inverse cosine is not defined for values less than -1 or greater than 1.
Does this calculator show degrees or radians?
Yes. This calculator shows the inverse cosine answer in both degrees and radians.
What is cos inverse of 0.5?
The cos inverse of 0.5 is 60 degrees, which is equal to approximately 1.0472 radians.
Is cos inverse the same as 1 divided by cos?
No. cos-1(x) means inverse cosine or arccos, not 1 divided by cosine. The reciprocal of cosine is secant.